A fan oscillates 250* and can be felt from a distance of 4 feet away . To the nearest tenth what area of the room can feel the wind from the fan? Use 3.14 for pi .

Question

asked May 21, 2022 8.7k views

1 Answer

Ilario Engler · Answer 1 · 2022-05-26T01:23:10+0000

Answer:

A=256.67ft^2

Explanation:

From the question we are told that:

Fan oscillates
$\theta=250$

Distance
$d=>Raduis\ r=4 feet$

Since

$250\textdegree =180\textdegree +70\textdegree$

Generally the equation for the area A is mathematically given by

$Area=Area\ of\ semi\ circle\ + area\ of\ 70\textdegree sector$

$A=A_(sm)+A_(70\textdegree)$

Where

$A_(sm)=(1)/(2) \pi r^2$

A_(sm)=(1)/(2) 3.14 4^2

A_(sm)=25.12ft^2

$A_(70\textdegree)=(1)/(2)r^2 (70\textdegree)/(360\textdegree)$

$A_(70\textdegree)=(1)/(2)*4^2* (70\textdegree)/(360\textdegree)$

$A_(70\textdegree)=1.55ft^2$

Therefore the area A is given as

$A=A_(sm)+A_(70\textdegree)$

A=25.12ft^2+1.55ft^2

A=256.67ft^2